where \(\theta \)  represents the network parameters, \(T\)  represents the Transformer, \(x\)  is the input and \(y\)  is the ground truth. Implementation and training of the proposed network were completed in Python 3.7.7 (Python Software Foundation) using the Pytorch library 1.8.1 [1]} on a computer with three NVIDIA Quadro RTX 8000 GPUs. The networks were trained for 100 epochs with a batch size of 400. An Adam optimizer with \(\beta _1=0.9\) , \(\beta _2=0.98\) , and \(\epsilon =10^{-9}\)  was used. The hyperparameters were \(d_{model}=1024\) , 16 attention heads, dimensions of keys and values \(d_k=64\) , \(d_v=64\) , dropout=0.1. The total training time was around 3 days. The reference data containing 400 spokes was regarded as the full k-space acquisition and was used to reconstruct the reference standard image.
